The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

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The Confrontation Between General Relativity and Experiment

Extremely narrow optical resonances in cold atoms or single trapped ions can be measured with high resolution. A laser locked to such a narrow optical resonance could serve as a highly stable oscillator for an all-optical atomic clock. However, until recently there was no reliable clockwork mechanism that could count optical frequencies of hundreds of terahertz. Techniques using femtosecond-laser frequency combs, developed within the past few years, have solved this problem. The ability to count optical oscillations of more than 1015 cycles per second facilitates high-precision optical spectroscopy, and has led to the construction of an all-optical atomic clock that is expected eventually to outperform today's state-of-the-art caesium clocks.

Optical frequency metrology

We stabilized the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. We confirmed control of the pulse-to-pulse carrier-envelope phase using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which we used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.

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Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis

Optical frequency combs provide equidistant frequency markers in the infrared, visible and ultraviolet, and can be used to link an unknown optical frequency to a radio or microwave frequency reference. Since their inception, frequency combs have triggered substantial advances in optical frequency metrology and precision measurements and in applications such as broadband laser-based gas sensing and molecular fingerprinting. Early work generated frequency combs by intra-cavity phase modulation; subsequently, frequency combs have been generated using the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized. Here we report a substantially different approach to comb generation, in which equally spaced frequency markers are produced by the interaction between a continuous-wave pump laser of a known frequency with the modes of a monolithic ultra-high-Q microresonator via the Kerr nonlinearity. The intrinsically broadband nature of parametric gain makes it possible to generate discrete comb modes over a 500-nm-wide span (approximately 70 THz) around 1,550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3 x 10(-18). In contrast to femtosecond mode-locked lasers, this work represents a step towards a monolithic optical frequency comb generator, allowing considerable reduction in size, complexity and power consumption. Moreover, the approach can operate at previously unattainable repetition rates, exceeding 100 GHz, which are useful in applications where access to individual comb modes is required, such as optical waveform synthesis, high capacity telecommunications or astrophysical spectrometer calibration.

Optical frequency comb generation from a monolithic microresonator

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist

Quantum sensing

A twentyfold improvement in the accuracy of a single ytterbium ion atomic clock is achieved using the ion's electric octupole transition.

Single-Ion Atomic Clock with 3 × 10 − 18 Systematic Uncertainty

Single-ion clocks yield new limits on how much the proton-to-electron mass ratio and the fine structure constant change over time.

Improved Limit on a Temporal Variation of m p / m e from Comparisons of Yb + and Cs Atomic Clocks

The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant $\ensuremath{\alpha}$ in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in $^{171}\mathrm{Y}\mathrm{b}^{+}$ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio ${f}_{\mathrm{Y}\mathrm{b}}/{f}_{\mathrm{C}\mathrm{s}}$ of $(\ensuremath{-}1.2\ifmmode\pm\else\textpm\fi{}4.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{y}\mathrm{r}}^{\ensuremath{-}1}$, consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of $\ensuremath{\alpha}$ at the level of $2.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}\text{ }{\mathrm{y}\mathrm{r}}^{\ensuremath{-}1}$ $(1\ensuremath{\sigma})$, corresponding so far to the most stringent limit from laboratory experiments.

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Limit on the Present Temporal Variation of the Fine Structure Constant

We introduce a novel concept for optical frequency measurement and division which employs a Kerr-lens, mode-locked laser as a transfer oscillator whose noise properties do not enter the measurement process. We experimentally demonstrate that this method opens up the route to phase-link signals with arbitrary frequencies in the optical or microwave range while their frequency stability is preserved.

Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements

We have determined the frequency of the $^{3}P_{1}$- $^{1}S_{0}$ intercombination transition of atomic ${}^{40}\mathrm{Ca}$ stored in a magneto-optical trap to be $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}455986240493.95\mathrm{kHz}$ with an estimated standard uncertainty of $0.43\mathrm{kHz}$ $(\ensuremath{\delta}\ensuremath{\nu}/\ensuremath{\nu}l{10}^{\ensuremath{-}12})$ using a phase-coherent optical frequency chain from the Cs atomic clock to the visible. This allows the realization of the SI-unit meter according to its definition by visible radiation with 25-fold reduced uncertainty compared to previous measurements.

Burghard Lipphardt

Papers

Single-Ion Atomic Clock with 3 × 10 − 18 Systematic Uncertainty

Improved Limit on a Temporal Variation of m p / m e from Comparisons of Yb + and Cs Atomic Clocks

Limit on the Present Temporal Variation of the Fine Structure Constant

Kerr-lens, mode-locked lasers as transfer oscillators for optical frequency measurements

First phase-coherent frequency measurement of visible radiation.